In both classical and boundary Yamabe problems, as a corollary of
the compactness of solutions, people get that the problem is also
stable for perturbation from below of the critical exponent. So stability
is proved for scalar flat manifolds in [1]}, for manifolds
with non umbilic boundary in [2]}, [3]}, and for umbilic boundary
manifolds whose Weyl tensor never vanishes on \(\partial M\)  in [4]}, [5]}.
On the other hand, in the present paper (and in [6]} for
umbilic boundary manifolds) we prove that Yamabe boundary problem
is unstable with respect of perturbation form above of the critical
exponent.
